In real research, continuous outcome measures may have a large number of observed values clustered at zero (also known as a semi-continuous outcome measure). Modeling such outcomes has long been a challenge in statistical analysis. Log-transformation cannot solve the problem of extra zeros in the measure, while recoding data into a dichotomous categorical variable (0 vs. 1) for analysis using logistic regression would discard important information. Furthermore, the two-part model developed in econometrics in the early 1980s is often used to analyze data with a concentration of zero values (Duan et al., 1983). This econometric two-part model uses one equation (usually logistic or probit regression) to model the probability of having a nonzero value, and another equation (linear regression) to model the nonzero values, assuming two separate or unconnected models (Manning, Duan, and Rogers, 1987). In most instances, however, the likelihood of having a nonzero value (vs. zero value) and the amount or frequency of nonzero values observed in an outcome are likely to be correlated. By modeling the likelihood and amount separately, the econometric two-part model ignores this correlation, and thus may introduce biases into parameter estimates (Olsen and Schafer, 2001). To deal with this problem, Tooze, Grunwald, and Jones (2002) proposed the Mixed-Effect Mixed Distribution Model and developed a SAS macro program to fit the semi-continuous outcome in longitudinal data. Alternatively, ...

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